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1.
Olivier Poisson 《Mathematical Methods in the Applied Sciences》1999,22(9):773-790
Let 𝒩(μ) be the counting function of the eigenvalues associated with the self‐adjoint operator −∇(ρ(x, z)∇·) in the domain Ω = ℝ × ]0, h[, h > 0, with Neuman or Dirichlet conditions at z = 0, h. If ρ = 1 in the exterior of a bounded rectangular region 𝒪, that is, for ∣x∣ large, then 𝒩(μ) is known to be sublinear: the proof consists in the spectral analysis of a quadratic form obtained from a Green formula for −∇(ρ(x, z)∇·) on 𝒪. In our case, the medium is multistratified: the function ρ(x, z) satisfies ρ(x, z) = ρ(z) for ∣x∣ large. Since the direct use of the previous proof fails, we modify the quadratic form and obtain the estimate N(μ) ⩽ Cμ3/2. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
2.
Peter Friz Nicolas Victoir 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(6):775-785
We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case. 相似文献
3.
Let h ≥ 6 be an integer, let G be a 3-connected graph with ∣V(G)∣ ≥ h − 1, and let x and z be distinct vertices of G. We show that if for any nonadjacent distinct vertices u and v in V(G) − {x, z}, the sum of the degrees of u and v in G is greater than or equal to h, then for any subset Y of V(G) − {x, z} with ∣Y∣ ≤ 2, G contains a path which has x and z as its endvertices, passes through all vertices in Y, and has length at least h − 2. We also show a similar result for cycles in 2-connected graphs. 相似文献
4.
A finite set A = {a1 < … <an}? ? is said to be convex if the sequence (ai ? ai?1)ni=2 is strictly increasing. Using an estimate of the additive energy of convex sets, one can estimate the size of the sumset as ∣A + A∣ ? ∣A∣102/65, which slightly sharpens Shkredov’s latest result ∣A + A∣ ? ∣A∣58/37.
相似文献5.
We examine the problem of embedding a graph H as the center of a supergraph G, and we consider what properties one can restrict G to have. Letting A(H) denote the smallest difference ∣V(G)∣ - ∣V(H)∣ over graphs G having center isomorphic to H it is demonstrated that A(H) ≤ 4 for all H, and for 0 ≤ i ≤ 4 we characterize the class of trees T with A(T) = i. for n ≥ 2 and any graph H, we demonstrate a graph G with point and edge connectivity equal to n, with chromatic number X(G) = n + X(H), and whose center is isomorphic to H. Finally, if ∣V(H)∣ ≥ 9 and k ≥ ∣V(H)∣ + 1, then for n sufficiently large (with n even when k is odd) we can construct a k-regular graph on n vertices whose center is isomorphic to H. 相似文献
6.
John E Olson 《Journal of Number Theory》1984,18(1):110-120
Sums C = A + B of two finite sets in a (generally non-abelian) group are considered. The following two theorems are proved. 1. unless C + (?B + B) = C; 2. There is a subset S of C and a subgroup H such that ∣S∣ ≥ ∣A∣ + ∣B∣ ? ∣H∣, and either H + S = S or S + H = S. 相似文献
7.
《Journal of the Egyptian Mathematical Society》2014,22(3):348-351
In this paper, we introduced two new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution. Furthermore, we find estimates on the coefficients ∣a2∣ and ∣a3∣ for functions in these new subclasses. 相似文献
8.
We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L
2-norm of Brownian local times, and coincides with the large deviation obtained by Csörgö, Shi and Yor (1991) for self intersection local times of Brownian bridges. Our approach relies on a Feynman-Kac type large deviation for Brownian occupation time, certain localization techniques from Donsker-Varadhan (1975) and Mansmann (1991), and some general methods developed along the line of probability in Banach space. Our treatment in the case of random walks also involves rescaling, spectral representation and invariance principle. The law of the iterated logarithm for intersection local times is given as an application of our deviation results.Supported in part by NSF Grant DMS-0102238Supported in part by NSF Grant DMS-0204513
Mathematics Subject Classification (2000):Primary: 60J55; Secondary: 60B12, 60F05, 60F10, 60F15, 60F25, 60G17, 60J65 相似文献
9.
Nina Gantert 《Probability Theory and Related Fields》1994,98(1):7-20
Summary Using self-similarity of Brownian motion and its representation as a product measure on a binary tree, we construct a random sequence of probability measures which converges to the distribution of the Brownian bridge. We establish a large deviation principle for random fields on a binary tree. This leads to a class of probability measures with a certain self-similarity property. The same construction can be carried out forC[0, 1]-valued processes and we can describe, for instance, aC[0, 1]-valued Ornstein-Uhlenbeck process as a large deviation of Brownian sheet. 相似文献
10.
Alain-Sol Sznitman 《Probability Theory and Related Fields》1993,95(2):155-174
Summary We consider a Brownian motion moving in a random potential obtained by translating a given fixed non negative shape function at the points of a Poisson cloud. We derive the almost sure principal long time behavior of the expectation of the natural Feynman Kac functional, which is insensitive to the detail of the shape function. We also study the situation of hard obstacles where Brownian motion is killed once it comes within distancea of a point of the cloud. The nature of the results then changes between the case whena is small or large in connection with the presence, or absence of an infinite component in the complement of the obstacles. 相似文献
11.
12.
Rasmus Pagh 《Random Structures and Algorithms》2009,35(1):70-82
We define a family of functions F from a domain U to a range R to be dispersing if for every set S ? U of a certain size and random h ∈ F, the expected value of ∣S∣ – ∣h[S]∣ is not much larger than the expectation if h had been chosen at random from the set of all functions from U to R. We give near‐optimal upper and lower bounds on the size of dispersing families and present several applications where using such a family can reduce the use of random bits compared to previous randomized algorithms. A close relationship between dispersing families and extractors is exhibited. This relationship provides good explicit constructions of dispersing hash functions for some parameters, but in general the explicit construction is left open. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009 相似文献
13.
In this paper we consider the Skorokhod embedding problem for target distributions with non-zero mean. In the zero-mean case,
uniform integrability provides a natural restriction on the class of embeddings, but this is no longer suitable when the target
distribution is not centred. Instead we restrict our class of stopping times to those which are minimal, and we find conditions
on the stopping times which are equivalent to minimality.
We then apply these results, firstly to the problem of embedding non-centred target distributions in Brownian motion, and
secondly to embedding general target laws in a diffusion.
We construct an embedding (which reduces to the Azema-Yor embedding in the zero-target mean case) which maximises the law
of sups≤TBs among the class of minimal embeddings of a general target distribution μ in Brownian motion. We then construct a minimal embedding of μ in a diffusion X which maximises the law of sups≤Th(Xs) for a general function h. 相似文献
14.
15.
It is shown in this paper that the Schrodinger operator with a potential satisfying ∣V(x)∣ ≤ M/∣x∣2a.e. in the unit ball B has the strong unique continuation property in H2,2(B) for for n≥2. 相似文献
16.
Jack Schaeffer 《Mathematical Methods in the Applied Sciences》2003,26(4):273-296
A collisionless plasma is modelled by the Vlasov–Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as ∣x∣ tends to infinity is considered. Hence, the total positive charge and the total negative charge are infinite. Smooth solutions with appropriate asymptotic behaviour were shown to exist locally in time in a previous work. This paper studies the time behaviour of the net charge and a natural quantity related to energy, and shows that neither is constant in time in general. Also, neither quantity is positive definite. When the background density is a decreasing function of ∣v∣, a positive definite quantity is constructed which remains bounded. A priori bounds are obtained from this. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
17.
《Quaestiones Mathematicae》2013,36(3):445-449
AbstractSome variations of Arhangel'skii inequality ∣X∣ = 2χ(X)L(X) for every Hausdorff space X [3], given in [2] and [6] are improved. 相似文献
18.
Ron Aharoni 《Graphs and Combinatorics》1993,9(2-4):209-212
A strengthened version of a previous conjecture of the author is considered. The former version of the conjecture was that if every subset of a given setA of vertices in a hypergraph is connected to a set of edges with ‘large’ matching number, thenA is matchable. Here we suggest that it is possible to assume only large fractional matching numbers. We prove the conjecture in the case ∣A∣ = 2, and also a fractional version of the conjecture. 相似文献
19.
In this paper, we first prove Schilder's theorem in Hölder norm (0 ≤ α <1) with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology. 相似文献